Given the Celsius to Fahrenheit formula:
\[ F = \frac{9}{5}C + 32 \]
Let's solve this equation for \( C \):
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Subtract 32 from both sides: \[ F - 32 = \frac{9}{5}C \]
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Multiply both sides by \( \frac{5}{9} \) (which is equivalent to dividing by \( \frac{9}{5} \)): \[ C = \frac{5}{9}(F - 32) \]
This expression can be written as: \[ C = \frac{5}{9}F - \frac{5}{9} \cdot 32 \] But it is not necessary to distribute 5/9 in the context of solving for \( C \).
Now we can check each statement regarding the steps taken:
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First step is to multiply by 9 on each side.
- False: The first step is to subtract 32 from both sides, not to multiply.
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First step is to add 32 to both sides.
- False: The first step is to subtract 32 from both sides.
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The next step from \( F - 32 = \frac{9}{5} C \), could be to multiply both sides by 5.
- False: The correct operation is to multiply both sides by \( \frac{5}{9} \) to isolate \( C \).
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The next step from \( F - 32 = \frac{9}{5} C \), could be to divide both sides by 5.
- False: The step here involves multiplying by \( \frac{5}{9} \), not dividing by 5.
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Solution: \( \frac{5}{9}F - 32 = C \)
- False: The correct expression should be written as \( C = \frac{5}{9}(F - 32) \) instead, which clearly shows the relation.
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To solve this equation for C, you would have to distribute at some point.
- False: While you can distribute after arriving at the expression \( C = \frac{5}{9}(F - 32) \), it's not necessary to solve for \( C \) in its isolated form. The most simplified isolated form of \( C \) can be kept as \( C = \frac{5}{9}(F - 32) \).
In summary, all of the provided statements are false.